Invariants
Level: | $88$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}3&84\\76&1\end{bmatrix}$, $\begin{bmatrix}11&68\\40&17\end{bmatrix}$, $\begin{bmatrix}31&8\\0&83\end{bmatrix}$, $\begin{bmatrix}33&32\\4&75\end{bmatrix}$, $\begin{bmatrix}79&84\\52&67\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.48.1.n.2 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $24$ |
Cyclic 88-torsion field degree: | $480$ |
Full 88-torsion field degree: | $211200$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-4.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
88.48.0-4.b.1.3 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.0-88.l.1.8 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.0-88.l.1.13 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.1-88.d.1.2 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.48.1-88.d.1.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
88.192.1-88.a.1.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.a.2.6 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.g.1.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.g.2.7 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.r.1.4 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.r.2.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.w.1.4 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.w.2.5 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.3-88.j.1.7 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.j.2.7 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.l.1.4 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.l.2.4 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.o.1.8 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.o.2.6 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.q.1.8 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
88.192.3-88.q.2.5 | $88$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.1-264.e.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.e.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.y.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.y.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.bx.1.7 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.bx.2.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.cq.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.cq.2.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.bb.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bb.2.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bm.2.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bm.3.9 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bo.1.9 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bo.2.9 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bu.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.bu.2.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.288.9-264.cy.1.38 | $264$ | $3$ | $3$ | $9$ | $?$ | not computed |
264.384.9-264.bo.1.4 | $264$ | $4$ | $4$ | $9$ | $?$ | not computed |